1) Make a list of the units in Z16, and with each unit give its multiplicative inverse.

This is just "arithmetic" If, for example, 3 and x are multiplicative inverses, then 3x= 1 (mod 16) so 3x= 16n+ 1. 16+ 1= 17 is not a multiple of 16 but 2(16)+ 1= 33 is. It is 3(11) so the multiplicative inverse of 3 is 11. Similarly 16n+ 1 is a multiple of 5 for n= 4: 16(4)+ 1= 65= 5(13) so the multiplicative inverse of 5 is 13. 16(3)+1= 49= 7(7) so 7 is its own multiplicative inverse. 5(16)+ 1= 81= 9*9 so 9 is also its own multiplicative inverse. 15*15= 225= 14(16)+ 1 so 15 is also its own multiplicative inverse.

If p is even, then px- 16n is divisible by 2 no matter what x and n are so we can never have px- 16n= 1 or px= 16n+ 1. What does that tell you?